Question

Calculate the length of the apothem of a regular polygon. A

regular hexagon is shown. What is the length of the apothem,
rounded to the nearest inch? Recall that in a regular hexagon,
the length of the radius is equal to the length of each side of the
hexagon
10 in.
a
5 in
9 in
11 in
4 in

Answer 1

9 in

Explanation:

For an n-sided polygon, the length of the apothem is ...

a = r·cos(180°/n)

We assume your problem statement is saying the radius is 10 inches. For a hexagon, n=6 and we have ...

a = (10 in)cos(30°) ≈ 8.66 in

Rounded to the nearest inch, the apothem is 9 in.